In the first proof, we saw that when we consider the irreducible
information content of any partitioning of the Universe (defined as
everything that exists), it is not possible for that entire Universe to
be partitioned into two (or, obviously, more) non-empty irreducible sets
and have one contain a necessary and perfect representation
of the other. This was because entropy is an extensive quantity
- all of the information carrying capacity of the ``God channel'' is
being consumed by irreducibly specifying the God state and there
is none left over for specifying the not-God state. The God
channel can irreducibly encode the Universe only if it is the
irreducibly encoded Universe. One is led to a contradiction whether or
not one begins with the fully reduced Universe and attempts to partition
it or one begins with it partitioned, fully reduces each partition, and
then attempts to ``identify'' one part in the other, although this short
work contents itself only with the simplest sufficient proof and doesn't
examine all possible variants of partitioning on domains with various
dimensionality and cardinality. The problem is in the partitioning
itself - the moment the whole is broken up into two distinct parts,
at least one bit of entropy is introduced that differentiates one
part from the other even if the two sets are otherwise identical.

If God can perfectly visualize all non-God real existing things in Its
real existing but distinct ``mind's eye'' (anthropomorphizing, of
course, but what else can one do when thinking about knowledge), then it
knows that its knowledge is of those things (in Its mind) and is
not those things (outside of Its mind) - not to know this is to
not know all things. The map, after all, is not the territory -
God is as subject to this precept of General Semantics as any other
informational system. God's knowledge is therefore not complete - it
cannot know these things as they really are outside of Its mind,
its abstract knowledge is not the same as the territory itself any more
than your abstract knowledge is. Furthermore God cannot, as we
saw above, be certain that its visualization is in fact correct, that
its secret decoder ring is giving it the right values for the non-God
part as the mapping it defines is certainly not unique, the space of
possibilities it selects from is large, and recall, in this timeless view of things there is no such thing as looking. There
is only an enormous DVD, broken into two pieces, where even if one piece
contains a complete redundant copy of the data on the other there is no
way of knowing that from possession of the one piece only - even
if it is large and complex enough to contain a complete language and
encoding system that self-consistently says that it does: it could
simply be mistaken.

However, there is another way to prove the same conclusion in an
entirely different context. This proof similarly relies on the axioms
and definitions used in the first proof but in a very different way. To
them we add the axioms that support Gödel's theorem, as they
appear manifestly true for the Universe itself. Suppose then, as before,
that the existential Universe has a self-encoded irreducible state that
is capable of symbolically encoded self-reference. This is not a
terrible stretch, since you are a part of the Universe and you
are thinking about the Universe in symbolically encoded ways - it
is therefore empirically self-evident that this is true to any
mind thinking about itself and the Universe. The proof then follows as:

In order for God to possess complete abstract/symbolic knowledge
of the Universe, that knowledge must include an expression of
arithmetic, as the abstract expression of arithmetic manifestly exists
in human knowledge if nowhere else; God's knowledge could hardly be
complete if God cannot add two and two to get four. This body of
knowledge is therefore subject to Gödel's first (completeness)
theorem; since it is capable of the expression of arithmetic (and is in
any event intrinsically both complex and self-referential, containing
all human-known examples of Gödelian knots of unknowable
propositions or set-theoretic paradoxes as a simple subset) it can be
complete or consistent but not both.

God's knowledge of the Universe cannot therefore be symbolic (encoded in
any way that has to be decoded by a deductive process) and inconsistent
with the true state of the Universe and still be arguably correct
knowledge. The Universe is real and hence cannot be inconsistent
- it simply is what it is (timelessly). Neither can its symbolic
knowledge be incomplete or God is not omniscient and hence is not God.

This is a contradiction. God's knowledge of the Universe must be both
consistent and complete in order not to violate the definition of God
given above, but if that knowledge is indirect and symbolic, capable of
self-reference and encoded at a high level upon itself, Gödel's
theorem tells us that it can't be both complete and consistent.

God's omniscient knowledge of the Universe cannot, therefore, be
indirect and symbolic. Symbolic reduction and projection of the
existential reality (all state information) of the Universe into a
subset of the Universe as code that is necessarily
self-referential and capable of expressing arithmetic renders it
incomplete, inconsistent, or (most likely) both.

In order for God to be omniscient (and omnipresent and omnipotent), its
knowledge can only be direct knowledge of the Universe
itself as the Universe itself, complete and consistent by the
existential property of the Universe.

Therefore: If God exists, God is the Universe itself.

Another amusing corrolary comes from considering Gödel's second
(consistency) theorem:

If God can prove that its symbolic, encoded knowledge of the
Universe is consistent, then it isn't consistent. God can
therefore never be certain that any symbolic encoding of the
knowledge of the Universe (including itself) is consistent and hence
true.

Again, only existential, self-encoded information lacking any
partitioning and the consequently necessary layer of projective
abstraction is guaranteed to be complete and consistent when speaking of
the Universe.

We conclude that God's knowledge of the Universe (including itself) cannot therefore be a symbolic map or encoding of any sort, which
is a result that is entirely consistent with the information theoretic
analysis above. In addition to the entropy problem, the
self-referential symbolic representation suffices to trigger Gödel's
theorems so that true omniscience is literally impossible. Again,
let's try to illuminate the difficulty with a concrete example, this one
familiar to all readers as they contemplate their own knowledge of
the Universe.